One factor of the function f(x) = x3 − 9x2 + 20x − 12 is (x − 6). Describe how to find the x-intercepts and the y-intercept of the graph of f(x) without using technology. Show your work and include all intercepts in your answer.

If the point A(8,4) and B(-7,4) are located one the coordinate plane. Then the graph has been plotted and the distance between the points is 15 units

The first point = A(8,4)

The second point = B(-7,4)

Plot the point on the coordinate plane

The distance between the two points d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Where d is the distance between the two points

[tex](x_1,y_1)[/tex] is the coordinates of the first point

[tex](x_2,y_2)[/tex] is the coordinates of the second point

Substitute the values in the equation

The distance d = [tex]\sqrt{(-7-8)^2+(4-4)^2}[/tex]

= [tex]\sqrt{(-15)^2}[/tex]

= 15 units

Hence, If the point A(8,4) and B(-7,4) are located one the coordinate plane. Then the graph has been plotted and the distance between the points is 15 units

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Carbon sequestering technology has the main purpose of being used To remove carbon from the air and put it into the ground.

Find out more below.

Carbon Sequestering refers to various processes that are used to remove the carbon in the air. This carbon is then stored in various places such as the ground and the oceans.

Carbon Sequestering happens naturally such as the process of photosynthesis. Thanks to Carbon Sequestering technology however, humans are able to use the technology to reduce our carbon footprint on Earth.

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Answer:

10/3

Step-by-step explanation:

Let x be the value of the second rational number.  The first rational number is 2/3, and we are told that the sum of these numbers is 4:

x + 2/3 = 4

Therefore:

x + 2/3 = 4

x  = 4 - 2/3

x = 12/3 - 2/3

x = (10/3)

In the graph given, the line of reflection for the triangle XYZ and triangle X'Y'Z' is x=2.

Given, the coordinates of the triangle XYZ are:

X = (4,5)

Y = (6,3)

Z = (3,2)

and the coordinates of the triangle X'Y'Z' are:

X' = (0,5)

Y' = (-2,3)

Z' = (1,2)

for image of the triangle XYZ to get reflected and become X'Y'Z',

reflection of axis takes place.

But the images are not identical and symmetrical, so the reflection is not about y axis.

we check for x=2

hence reflection of axis when x=a is :

P(x,y) →x'(2a-x , y)

therefore use the above formula and check the coordinates of the reflected image.

X(4,5) → X'(2(2)-4 , 5)

x(4,5) → X'(0,5)

Y(6,3) → Y'(2(2)-6 , 3)

Y(6,3) → Y'(-2,3)

Z(3,2) → Z'(2(2)-3 , 2)

Z(3,2) → Z'(1,2)

hence x=2 is the reflection of triangle XYZ and X'Y'Z'.

Therefore we get the requires answer.

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Angles supplementary to ∠3 are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, and ∠7.

So, angles supplementary to ∠3:

(Refer to the image attached below)

Therefore, angles supplementary to ∠3 are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, and ∠7.

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Answer: Reduce 12/28 to the lowest terms The simplest form of 12 28 is 3 7.

Step-by-step explanation: I hope this helps!

Answer: y= 18

Step-by-step explanation:

5y/3 = 30
First step: multiply 3 on both sides

5y/3 * 3 = 30*3

5y = 90

Second step: divide 5 on both sides (isolating variable)

5y/5 = 90/5

y = 18

Answer:

y = 18

Step-by-step explanation:

[tex]\frac{5y}{3}[/tex] = 30 ( multiply both sides by 3 to clear the fraction )

5y = 3 × 30 = 90 ( divide both sides by 5 )

y = 18

Answer: 37.31 minutes

Step-by-step explanation:

Answer:

Step-by-step explanation:

Choose two points on the graph: (-6,-7) and (6,-9)

The straight line equation is: y=mx+b

[tex]\displaystyle\\\boxed {The\ slope\ m=\frac{y_2-y_1}{x_2-x_1} }\\\\x_1=-6\ \ \ \ x_2=6\ \ \ \ \ y_1=-7\ \ \ \ y_2=-9\\\\m=\frac{-9-(-7)}{6-(-6)} \\\\m=\frac{-9+7}{6+6} \\\\m=\frac{-2}{12} \\\\m=-\frac{1}{6}\\\\Hence,\ y=-\frac{1}{6}x+b\ \ \ \ \ (1)[/tex]

To determine the coefficient b, take any of the two points,

for example (-6,-7), that is, x=-6   y=-7

Substitute these values into formula (1):

[tex]\displaystyle\\-7=-\frac{1}{6}(-6) +b\\\\-7=1+b\\\\-7-1=1+b-1\\\\-8=b\\\\Thus,\ b=-8\\\\The\ result\ is\ y=-\frac{1}{6}x-8[/tex]

Answer:

C) x < -3

Step-by-step explanation:

-3x +12 < 4x - 9

-3x -4x < -12 - 9

-7x < -21

x > -3

If lines and m are parallel and lines s and t are parallel. If the measure of 21 is 35°, the measure of ∠2? is : D) 145°.

Based on the given figure ∠1 and ∠3  form a parallel line.

Now let determine the measure of  ∠2

Hence,

∠1+∠3=180 °

35°  +∠3= 180 °

∠3 =  180 ° - 35°

∠3 = 145 °

The corresponding angles is  ∠4 = ∠3  = 145 °

 ∠ 2 an  ∠ 4 are as well a  corresponding angles

So,

∠2 = ∠4 = 145 °

Therefore the we can conclude that the correct option is D.

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The correlation for r = -0.009 is B. weak negative.

The Pearson correlation coefficient (r) is the most commonly used metric for determining a linear relationship. It is a number ranging from -1 to 1 that indicates the strength and direction of a link between two variables. When one variable shifts, the other shifts in the same way.

Positive correlation is graded on a scale of 0.1 to 1.0. Weak positive correlation would be between 0.1 and 0.3, moderate positive correlation between 0.3 and 0.5, and strong positive correlation between 0.5 and 1.0. The stronger the positive correlation, the more probable the equities will move in unison. Having a minus means it's negative correlation.

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The company’s stock price today would be $33.46.

Dividend per share Year 1 (D1) = $3.30 per share

Dividend per share Year 2 (D2) = $2.52 per share

Stock Price for the Year 2 (P2) = D2(1 + g) / (Ke – g)

= $2.52(1 + 0.042) / (0.1160 – 0.042)

= $2.63 / 0.0740

= $35.48 per share

The company’s stock price is the Present Value of the future dividend payments and the present value the stock price for the year 2

The Stock Price = D1/(1 + r)1 + D2/(1 + r)2 + P2/(1 + r)2

= $3.30/(1 + 0.1160)1 + $2.52/(1 + 0.1160)2 + $35.48/(1 + 0.1160)2

= [$3.30 / 1.1160] + [$2.52 / 1.24546] + [$35.48 / 1.24546]

= $2.95 + $2.02 + $28.49

= $33.46 per share

Hence, the company’s stock price today would be $33.46.

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Answer: The answer is 1013, it is already rounded as much as it can go.

Step-by-step explanation:

Answer:

7+7+8

Step-by-step explanation:

9+4=13

35-13=22

22÷3 because they are three question mark

so 7 r 1

. .

. 4+7+9+7+8 =35

Answer: 12.8 miles per hour

Step-by-step explanation:

divide 16 by 1.25 in order to get your answer

Answer:

8n+16

Explanation:

Given the expressions:

First, distribute 8 over the terms in the bracket:

Finally, collect like terms and simplify:

An equivalent expression is 8n+16.

Answer:

a.) x = 5

b.) x = 35/2 = 17.5

Step-by-step explanation:

In both problems, we are trying to solve for x, which means we need to isolate it on one side of the equation.

a.) 5/2 x + 1 = 11

5/2 x = 10

Now to divide by a fraction is the same as multiplying by the reciprocal.

x = 10 * 2/5 = 4

b.) 2/7 x - 3 = 2

2/7 x = 5

To divide by a fraction is the same as multiplying by the reciprocal.

x = 5 * 7/2 = 35/2 = 17.5

Answer: it could literally be anything

Step-by-step explanation: if 4*z+7=15 then z=2

√49 = +/- 7

√16 = +/- 4 as you calculated

Congrats, you did it!

Given:

There are given that the two points:

Explanation:

According to the question:

We need to find the equation of the line:

Then,

To find the equation of the line, first, we need to find the slope of the line.

So,

From the formula of the slope of the line:

Where,

Then,

Put all the values into the given formula:

So,

Then,

From the formula of the equation of the line:

Then,

Put the value of m into the above equation:

So,

Then,

Final answer:

Hence, the equation of line is shown below:

The proportion of elementary school children who get between 9 and 10 hours of sleep per night is 0.6367 or 63.67%.

The amount of sleep that elementary school children get per night  be denoted by X, X follows a Normal distribution with a mean of 9.5 hours and a standard deviation of 0.55 hours.

the proportion of elementary school children who get between 9 and 10 hours of sleep per night is equal to

P(9≤ X ≤ 10) = P((9 - 9.50)/0.55 ≤ Z ≤ (10 - 9.50)/0.55)

P(9≤ X ≤ 10) = P(-0.9091 ≤ Z ≤ 0.9091)

P(9≤ X ≤ 10) = 0.6367

P(X > 12) = P(Z>(12 - 9.50)/0.55)

P(X > 12) = P(Z>4.5455

P(X> 12) = 0.000

THere is zero possibility of student to get more than 12 houtrs of sleep

The proportion of elementary school children who get between 9 and 10 hours of sleep per night is 0.6367 or 63.67%.

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An equation represents proportional relationship when dividing the quantities of the equation results in a quotient that is always the same.

Equation: y = mx and m is a constant value, which means is the same.

A. Equation: 120 - x = L

Equation from alternative A is NOT proportional since the division of the quantities doesn't result in a constant.

B. Equation: 1.08p = t

Dividing total cost per item's price, will always give the sales tax, which is constant. So, this equation IS proportional.

t/p=1.08

C. Equation: x=m/4

This equation is proportional because dividing marbles per how much each sister gets, always gives the number of sisters:

m/x=4

D. Equation: V= 12s^2

This equation is NOT proportional because side length is squared, so it is not constant linearly.

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Step-by-step explanation:

Given the formula below

The value of three-fourths + two-sixths is thirteen-twelfths or one and one-twelfth. Option D

A fraction can be defined as a part of a whole set or element.

There are several types of fractions which includes;

Examples of simple fractions; 1/ 2, 1/6

Examples of proper fractions; 2/3, 4/7

Examples of improper fractions; 4/3, 3/2

Examples of mixed fractions; 2 1/ 4, 7 1/2

From the information given, we have that;

3/ 4 + 2/ 6

Find the lowest common multiple

9 + 4 /12

13/ 12

Hence, the value is 13/12

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Answer:

Step-by-step explanation:

answer is the first one: square root property of equality

BTS zzz

Answer:

Reflexive property of equality

Step-by-step explanation:

look at the image

Given data:

The given expression for height is h=3t+2.

Substitute 30 for t in the above expression.

Thus, the height of the balloon after 30 seconds is 92 ft, so option (C) is correct.

Answer: (-3, 0)

Step-by-step explanation: Isolate the y variable, so you get 15y = 15 + 5x, then divide by 15, y = 1 + 1/3x. To get the x intercept, the y has to be equal to 0, so we get 0 = 1 + 1/3x.

0 = 1+1/3x

-1 = 1/3x

-3 = x

Answer:

x = - 3

Step-by-step explanation:

To get the x intercept, y has to be equal to 0.

- 5·x + 15·y = 15

- 5·x + 15·0 = 15

- 5·x = 15

x = 15/(- 5)

x = - 3